On Lightning Network and crypto

[EdgarNo]

My knowledge on crypto is not the best, but I read an article that VPN I'm using is teaming up with Litecoin and they use Lightning Network. It was praised for high transaction speed because it happens strictly p2p and the network itself is being "informed" only if the transaction is successful. In the wiki page it's written

"The payment channels allow participants to transfer money to each other without having to make all their transactions public on the blockchain. This is done by penalizing uncooperative participants. When opening a channel, participants must commit an amount (in a funding transaction, which is on the blockchain). Time-based script extensions like CheckSequenceVerify and CheckLockTimeVerify make the penalties possible."

I don't really understand how this penalty mechanism works. Do these two script extensions check if the requirements for the transaction are met and only then allow it to happen, am I understanding this right? And I don't understand for what purpose a VPN will be used here, just for security reasons or is there some deeper connection between VPN and Crypto? Thank you in advance.